非线性Rossby波所满足的三阶Zakharov方程与低频振荡

THREE ORDER ZAKHAROV EQUATION SATISFIED BY NONLINEAR ROSSBY WAVES IN THE BAROTROPIC ATMOSPHERE AND LOW FREQUENCY OSCILLATION

本文在基本气流具有水平切变的情况下,利用摄动法导出了非线性Rossby波所满足的三阶Zakharov方程,然后,考虑了基流具有弱切变的情况,通过使用三阶Zakharov方程研究了Rossby波列的第一类不稳定性问题。结果表明:通过非线性作用,大气中的Rossby波列可产生调制不稳定。同时,本文对这种不稳定的区域,增长率和周期进行了详细的计算,并讨论了波振幅、波数、纬度和基流切变对它们的影响,指出Rossby波列的调制不稳定可以激发30～60天的低频振荡。

In this paper, the perturbation method is used to derive three order Zakharov equation satisfied by nonlinear Rossby waves with horizontal shear basic flow. For the case of weak horizontal shear, the three order Zakharov equation is applied to investigate the first class instabilities of Rossby wave trains, and the results show that Rossby wave trains may produce modulational instability due to nonlinear effect . Furthermore , the instability region , growth rate and periods of Rossby wave trains are caculated,and the effects of waveamplitude, wavenumbers, latitude and basic flow shear are dicussed. It is found that the modulational instability of Rossby wave trains can excite 30-60 day low frequency oscillation.